By Tutte [1]}, each connected vertex-transitive and edge-transitive graph of odd valency is arc-transitive. So half-arc-transitive graphs of odd valency do not exist. Bouwer [2]} answered Tutte's question about existence of half-arc-transitive graphs of even valency. A number of authors later studied the construction of these graphs. See, for example [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. Let \(p\)  be a prime. There are no
half-arc-transitive graphs of order \(p\) , \(p^{2}\)  and \(2p\)  (see [15]}, [16]}). Feng, Kwak, Wang
and Zhou [17]} classified the connected tetravalent half-arc-transitive
graphs of order \(2pq\)  for distinct odd primes \(p\)  and \(q\) . The tetravalent half-arc-transitive graphs of order
\(p^{5}\) , \(p^{4}\) , \(2p^{2}\) , \(p^{3}\)  and \(2p^{3}\)  are classified in [18]}, [19]}, [20]}, [21]}, [22]} respectively. Wang et al. [23]} studied
tetravalent half-arc-transitive graphs of order a product of three primes. In [24]}, Liu studied tetravalent half-arc-transitive graphs of order \(p^{2}q^{2}\)  with \(p\) , \(q\)  distinct odd primes. Feng et al. [25]} classified the tetravalent
half-arc-transitive graphs of order \(4p\) . In [26]} a complete classification of tetravalent half-arc-transitive
metacirculants of order 2-powers was given. In [27]}, a classification of all tetravalent half-arc-transitive graphs of
order \(8p\)  was given. In this paper, we will study tetravalent half-arc-transitive graphs of order \(12p\) .
